# -*- Mode: shell-script -*-
#############################################################################
##
#A  trans13.grp                  GAP group library           Alexander Hulpke
#A                                                              & John Conway
##
##
#Y  Copyright (C) 2018-2021, Carnegie Mellon University
#Y  All rights reserved.  See LICENSE for details.
#Y  
#Y  This work is based on GAP version 3, with some files from version 4.  GAP is
#Y  Copyright (C) (1987--2021) by the GAP Group (www.gap-system.org).
##
##  This file contains the transitive groups of degree 13.
##

TRANSGRP[13]:= [
[(1,2,3,4,5,6,7,8,9,10,11,12,13),"C(13) = 13"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),
(1,12)(2,11)(3,10)(4,9)(5,8)(6,7),"D(13) = 13:2"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),
(1,3,9)(2,6,5)(4,12,10)(7,8,11),"F_39(13) = 13:3"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),
(1,5,12,8)(2,10,11,3)(4,7,9,6),"F_52(13) = 13:4"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),
(1,4,3,12,9,10)(2,8,6,11,5,7),"F_78(13) = 13:6"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),
(1,2,4,8,3,6,12,11,9,5,10,7),"F_156(13) = 13:12"],
[(1,2,3,4,5,6,7,8,9,10,11,12,13),(2,12)(4,11)(5,6)(7,10),"L(13) = PSL(3,3)"],
[(1,12,13),(2,12,13),(3,12,13),(4,12,13),(5,12,13),(6,12,13),
(7,12,13),(8,12,13),(9,12,13),(10,12,13),(11,12,13),"A(13)"],
[(1,13),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,10),
(10,11),(11,12),"S(13)"]];

TRANSPROPERTIES[13]:=
[[13,1,1,1,[F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,T],[5013],[11013],[21013]],
[26,1,1,1,[F,F,F,F,F,T,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,T],[5013],[-5026],[-7026,5013]],
[39,1,1,1,
[F,F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
T,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,T],
[1039],[3039],[3013,5039]],
[52,1,1,-1,[F,F,F,F,F,T,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,T,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,T],[-2026],[-2052],[-3052,-2026]],
[78,1,1,1,
[F,F,F,F,F,T,F,F,F,F,
F,F,F,F,F,F,F,F,F,
T,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,T,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,T],
[1039],[-1078],[-1078,-1026,1039]],
[156,1,2,-1,[F,F,F,F,F,T,F,F,
F,F,F,F,F,F,F,F,F,
F,F,T,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,T,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,T,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
T,T],[-78],[-156],[-156,-78,-52]],
[5616,1,2,1,
[F,F,F,T,F,F,F,F,F,F,
F,F,F,F,F,F,T,F,F,T,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,T,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,T,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F,F,
F,F,F,T,F,F,F,F,F,
F,F,F,F,F,F,F,T],[78],
[156],[52,234]],
[3113510400,1,11,1,[F,T,F,T,F,T,T,
F,T,F,T,F,T,F,T,F,T,
F,T,T,F,T,F,T,F,F,T,
F,T,F,T,F,T,F,T,T,F,
F,T,F,T,F,T,T,F,T,T,
F,F,T,F,F,T,T,F,T,F,
T,F,T,F,T,F,F,T,F,T,
F,T,T,T,F,T,F,T,F,T,
F,T,T,F,F,T,F,F,T,T,
F,T,F,T,T,F,F,T,F,T,
F,F,T],[78],[156],[286]],
[6227020800,1,13,-1,
[T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T,T,T,T,T,T,T,T,T,T,T,
T],[-78],[-156],[-286]]];

